License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.775
URN: urn:nbn:de:0030-drops-53357
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5335/
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Felber, David ; Ostrovsky, Rafail

A Randomized Online Quantile Summary in O(1/epsilon * log(1/epsilon)) Words

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Abstract

A quantile summary is a data structure that approximates to epsilon-relative error the order statistics of a much larger underlying dataset.

In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O((1/epsilon) log(1/epsilon)) words of memory. This improves upon the previous best upper bound of O((1/epsilon) (log(1/epsilon))^(3/2)) by Agarwal et al. (PODS 2012). Further, by a lower bound of Hung and Ting (FAW 2010) no deterministic summary for the comparison model can outperform our randomized summary in terms of space complexity. Lastly, our summary has the nice property that O((1/epsilon) log(1/epsilon)) words suffice to ensure that the success probability is 1 - exp(-poly(1/epsilon)).

BibTeX - Entry

@InProceedings{felber_et_al:LIPIcs:2015:5335,
  author =	{David Felber and Rafail Ostrovsky},
  title =	{{A Randomized Online Quantile Summary in O(1/epsilon * log(1/epsilon)) Words}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{775--785},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5335},
  URN =		{urn:nbn:de:0030-drops-53357},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.775},
  annote =	{Keywords: order statistics, data stream, streaming algorithm}
}

Keywords: order statistics, data stream, streaming algorithm
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 13.08.2015

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